What is 2/6 plus 9/26? (Answer: 53/78)

Exact Answer

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Problem: What is 2/6 plus 9/26?
Formula / Expression: 2/6 + 9/26
Final Answer: 53/78
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Step-by-Step Solution:

Step 1: Find the Least Common Denominator (LCD)
The denominators 6 and 26 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 78 (which is smaller than their product 6 × 26 = 156, keeping the calculation simpler).
Working: LCD(6, 26) = 78

Step 2: Convert to Equivalent Fractions with Common Denominator 78
Multiply the numerator and denominator of 2/6 by 13, and multiply the numerator and denominator of 9/26 by 3 so both fractions share the common base 78.
Working: 2 × 13/6 × 13 = 26/78 and 9 × 3/26 × 3 = 27/78

Step 3: Add the Numerators
Now add the numerators (26 + 27 = 53) and keep the common denominator 78 unchanged.
Working: 26 + 27/78 = 53/78

Step 4: Check if the Fraction Can Be Simplified
The Greatest Common Divisor (GCD) of 53 and 78 is 1, confirming that 53/78 cannot be reduced further—it is already in its simplest irreducible form.
Working: 53/78

Step 5: Decimal & Percentage Representation
Dividing the numerator 53 by denominator 78 produces a repeating decimal (approximately 0.679487, or 67.9487%).
Working: 53 ÷ 78 = 0.679487 (67.9487%)

Key Values:
- Simplified Fraction: 53/78
- Mixed Number Form: 53/78
- Decimal Value: 0.679487
- Percentage: 67.9487%

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Solved with FractionsCalc:
https://fractionscalc.com/what-is-2-6-plus-9-26/
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2/6 + 9/26 = 53/78

Simplified Fraction

53/78

Mixed Number

Proper (53/78)

Decimal Value

0.679487

Percentage

67.9487%

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Step-by-Step Solution: 2/6 + 9/26

Step 1

Find the Least Common Denominator (LCD)

The denominators 6 and 26 share a common factor (GCD = 2). Finding their Least Common Multiple gives an LCD of 78 (which is smaller than their product 6 × 26 = 156, keeping the calculation simpler).

LCD(6, 26) = 78

Step 2

Convert to Equivalent Fractions with Common Denominator 78

Multiply the numerator and denominator of 2/6 by 13, and multiply the numerator and denominator of 9/26 by 3 so both fractions share the common base 78.

2 × 13/6 × 13 = 26/78 and 9 × 3/26 × 3 = 27/78

Step 3

Add the Numerators

Now add the numerators (26 + 27 = 53) and keep the common denominator 78 unchanged.

26 + 27/78 = 53/78

Step 4

Check if the Fraction Can Be Simplified

The Greatest Common Divisor (GCD) of 53 and 78 is 1, confirming that 53/78 cannot be reduced further—it is already in its simplest irreducible form.

53/78

Step 5

Decimal & Percentage Representation

Dividing the numerator 53 by denominator 78 produces a repeating decimal (approximately 0.679487, or 67.9487%).

53 ÷ 78 = 0.679487 (67.9487%)

Visual Representation

The diagram below illustrates 2/6 plus 9/26 visually:

Summary & Alternative Representations

Property / Format	Value
Lowest Terms Fraction	`53/78`
Mixed Number Form	`53/78`
Decimal Form	`0.679487`
Percentage	`67.9487%`

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Frequently Asked Questions

What is 2/6 plus 9/26 as a fraction?

2/6 + 9/26 in simplest fraction form is 53/78.

What is 2/6 plus 9/26 as a decimal?

2/6 + 9/26 converted to a decimal is 0.679487.

What is 2/6 plus 9/26 as a percentage?

2/6 + 9/26 expressed as a percentage is 67.9487%.

Does 2/6 plus 9/26 result in a terminating or repeating decimal?

It results in a repeating decimal (approximately 0.679487...) because the denominator contains prime factors other than 2 and 5.